What is the value of ( 997^2 )?
Answer and explanation
Correct answer: 994009
Write 997 as \(1000-3\). Using \((a-b)^2=a^2-2ab+b^2\), \((1000-3)^2=1000^2-2\times1000\times3+3^2=1000000-6000+9=994009\). Therefore, the correct answer is 994009. The value 997009 results from an incorrect middle-term calculation. Exam tip: use \((a-b)^2\) for squaring numbers close to 1000.
Frequently asked questions
What is the correct answer to this question?
994009
Why is this the correct answer?
Write 997 as \(1000-3\). Using \((a-b)^2=a^2-2ab+b^2\), \((1000-3)^2=1000^2-2\times1000\times3+3^2=1000000-6000+9=994009\). Therefore, the correct answer is 994009. The value 997009 results from an incorrect middle-term calculation. Exam tip: use \((a-b)^2\) for squaring numbers close to 1000.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Algebraic identities.
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